TSTP Solution File: SEU611^2 by Leo-III-SAT---1.7.15
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.15
% Problem : SEU611^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d SAT
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 15:32:13 EDT 2024
% Result : Theorem 4.71s 2.03s
% Output : Refutation 4.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 12 unt; 0 typ; 4 def)
% Number of atoms : 104 ( 8 equ; 0 cnn)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 325 ( 40 ~; 32 |; 0 &; 217 @)
% ( 0 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 61 ( 7 ^ 54 !; 0 ?; 61 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_type,type,
in: $i > $i > $o ).
thf(dsetconstr_type,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(dsetconstrEL_type,type,
dsetconstrEL: $o ).
thf(dsetconstrEL_def,definition,
( dsetconstrEL
= ( ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ ( dsetconstr @ A @ B ) )
=> ( in @ C @ A ) ) ) ) ).
thf(dsetconstrER_type,type,
dsetconstrER: $o ).
thf(dsetconstrER_def,definition,
( dsetconstrER
= ( ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ ( dsetconstr @ A @ B ) )
=> ( B @ C ) ) ) ) ).
thf(binunion_type,type,
binunion: $i > $i > $i ).
thf(binunionE_type,type,
binunionE: $o ).
thf(binunionE_def,definition,
( binunionE
= ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( binunion @ A @ B ) )
=> ( ( in @ C @ A )
| ( in @ C @ B ) ) ) ) ) ).
thf(symdiff_type,type,
symdiff: $i > $i > $i ).
thf(symdiff_def,definition,
( symdiff
= ( ^ [A: $i,B: $i] :
( dsetconstr @ ( binunion @ A @ B )
@ ^ [C: $i] :
( ~ ( in @ C @ A )
| ~ ( in @ C @ B ) ) ) ) ) ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(sk4_type,type,
sk4: $o ).
thf(1,conjecture,
( dsetconstrEL
=> ( dsetconstrER
=> ( binunionE
=> ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( symdiff @ A @ B ) )
=> ! [D: $o] :
( ( ( in @ C @ A )
=> ( ~ ( in @ C @ B )
=> D ) )
=> ( ( ~ ( in @ C @ A )
=> ( ( in @ C @ B )
=> D ) )
=> D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffE) ).
thf(2,negated_conjecture,
~ ( dsetconstrEL
=> ( dsetconstrER
=> ( binunionE
=> ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( symdiff @ A @ B ) )
=> ! [D: $o] :
( ( ( in @ C @ A )
=> ( ~ ( in @ C @ B )
=> D ) )
=> ( ( ~ ( in @ C @ A )
=> ( ( in @ C @ B )
=> D ) )
=> D ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ ( dsetconstr @ A @ B ) )
=> ( in @ C @ A ) )
=> ( ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ ( dsetconstr @ A @ B ) )
=> ( B @ C ) )
=> ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( binunion @ A @ B ) )
=> ( ( in @ C @ A )
| ( in @ C @ B ) ) )
=> ! [A: $i,B: $i,C: $i] :
( ( in @ C
@ ( dsetconstr @ ( binunion @ A @ B )
@ ^ [D: $i] :
( ~ ( in @ D @ A )
| ~ ( in @ D @ B ) ) ) )
=> ! [D: $o] :
( ( ( in @ C @ A )
=> ( ~ ( in @ C @ B )
=> D ) )
=> ( ( ~ ( in @ C @ A )
=> ( ( in @ C @ B )
=> D ) )
=> D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,plain,
( in @ sk3
@ ( dsetconstr @ ( binunion @ sk1 @ sk2 )
@ ^ [A: $i] :
( ~ ( in @ A @ sk1 )
| ~ ( in @ A @ sk2 ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(8,plain,
! [C: $i,B: $i > $o,A: $i] :
( ~ ( in @ C @ ( dsetconstr @ A @ B ) )
| ( in @ C @ A ) ),
inference(cnf,[status(esa)],[3]) ).
thf(123,plain,
! [C: $i,B: $i > $o,A: $i] :
( ( in @ C @ A )
| ( ( in @ sk3
@ ( dsetconstr @ ( binunion @ sk1 @ sk2 )
@ ^ [D: $i] :
( ~ ( in @ D @ sk1 )
| ~ ( in @ D @ sk2 ) ) ) )
!= ( in @ C @ ( dsetconstr @ A @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[10,8]) ).
thf(124,plain,
in @ sk3 @ ( binunion @ sk1 @ sk2 ),
inference(pattern_uni,[status(thm)],[123:[bind(A,$thf( binunion @ sk1 @ sk2 )),bind(B,$thf( ^ [D: $i] : ( ~ ( in @ D @ sk1 ) | ~ ( in @ D @ sk2 ) ) )),bind(C,$thf( sk3 ))]]) ).
thf(7,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ ( binunion @ A @ B ) )
| ( in @ C @ A )
| ( in @ C @ B ) ),
inference(cnf,[status(esa)],[3]) ).
thf(12,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ ( binunion @ A @ B ) )
| ( in @ C @ A )
| ( in @ C @ B ) ),
inference(simp,[status(thm)],[7]) ).
thf(166,plain,
! [C: $i,B: $i,A: $i] :
( ( in @ C @ A )
| ( in @ C @ B )
| ( ( in @ sk3 @ ( binunion @ sk1 @ sk2 ) )
!= ( in @ C @ ( binunion @ A @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[124,12]) ).
thf(167,plain,
( ( in @ sk3 @ sk1 )
| ( in @ sk3 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[166:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 )),bind(C,$thf( sk3 ))]]) ).
thf(6,plain,
( ( in @ sk3 @ sk1 )
| ~ ( in @ sk3 @ sk2 )
| sk4 ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
( ~ ( in @ sk3 @ sk1 )
| ( in @ sk3 @ sk2 )
| sk4 ),
inference(cnf,[status(esa)],[3]) ).
thf(4,plain,
~ sk4,
inference(cnf,[status(esa)],[3]) ).
thf(78,plain,
( ~ ( in @ sk3 @ sk1 )
| ( in @ sk3 @ sk2 )
| $false ),
inference(rewrite,[status(thm)],[5,4]) ).
thf(79,plain,
( ~ ( in @ sk3 @ sk1 )
| ( in @ sk3 @ sk2 ) ),
inference(simp,[status(thm)],[78]) ).
thf(9,plain,
! [C: $i,B: $i > $o,A: $i] :
( ~ ( in @ C @ ( dsetconstr @ A @ B ) )
| ( B @ C ) ),
inference(cnf,[status(esa)],[3]) ).
thf(11,plain,
! [C: $i,B: $i > $o,A: $i] :
( ~ ( in @ C @ ( dsetconstr @ A @ B ) )
| ( B @ C ) ),
inference(simp,[status(thm)],[9]) ).
thf(14,plain,
! [C: $i,B: $i > $o,A: $i] :
( ( B @ C )
| ( ( in @ sk3
@ ( dsetconstr @ ( binunion @ sk1 @ sk2 )
@ ^ [D: $i] :
( ~ ( in @ D @ sk1 )
| ~ ( in @ D @ sk2 ) ) ) )
!= ( in @ C @ ( dsetconstr @ A @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[10,11]) ).
thf(15,plain,
( ~ ( in @ sk3 @ sk1 )
| ~ ( in @ sk3 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[14:[bind(A,$thf( binunion @ sk1 @ sk2 )),bind(B,$thf( ^ [D: $i] : ( ~ ( in @ D @ sk1 ) | ~ ( in @ D @ sk2 ) ) )),bind(C,$thf( sk3 ))]]) ).
thf(38,plain,
( ~ ( in @ sk3 @ sk1 )
| ~ ( in @ sk3 @ sk2 ) ),
inference(cnf,[status(esa)],[15]) ).
thf(82,plain,
( ~ ( in @ sk3 @ sk1 )
| ( ( in @ sk3 @ sk2 )
!= ( in @ sk3 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[79,38]) ).
thf(83,plain,
~ ( in @ sk3 @ sk1 ),
inference(pattern_uni,[status(thm)],[82:[]]) ).
thf(113,plain,
( $false
| ~ ( in @ sk3 @ sk2 )
| $false ),
inference(rewrite,[status(thm)],[6,83,4]) ).
thf(114,plain,
~ ( in @ sk3 @ sk2 ),
inference(simp,[status(thm)],[113]) ).
thf(174,plain,
( $false
| $false ),
inference(rewrite,[status(thm)],[167,114,83]) ).
thf(175,plain,
$false,
inference(simp,[status(thm)],[174]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU611^2 : TPTP v8.2.0. Released v3.7.0.
% 0.04/0.12 % Command : run_Leo-III %s %d SAT
% 0.12/0.33 % Computer : n017.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 21 13:03:10 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.95/0.86 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.20/0.97 % [INFO] Parsing done (104ms).
% 1.20/0.98 % [INFO] Running in sequential loop mode.
% 1.63/1.17 % [INFO] nitpick registered as external prover.
% 1.63/1.17 % [INFO] Scanning for conjecture ...
% 1.84/1.24 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.84/1.26 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.84/1.26 % [INFO] Problem is higher-order (TPTP THF).
% 1.84/1.26 % [INFO] Type checking passed.
% 1.84/1.27 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 4.71/2.02 % [INFO] Killing All external provers ...
% 4.71/2.02 % Time passed: 1489ms (effective reasoning time: 1044ms)
% 4.71/2.02 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 4.71/2.02 % Axioms used in derivation (0):
% 4.71/2.02 % No. of inferences in proof: 27
% 4.71/2.03 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1489 ms resp. 1044 ms w/o parsing
% 4.71/2.06 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.71/2.06 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------